= Entropy of a hyperbolic toral automorphism
{title2=$h_{\mathrm{top}}(A)=\log|\lambda_u|\quad(A\in\mathrm{GL}(2,\mathbb Z))$}
For a two-dimensional <hyperbolic toral automorphism>, the stable and unstable <eigenvalues> obey $|\lambda_s|<1<|\lambda_u|$. In a sufficiently small <Bowen ball>, lifting to the stable and unstable coordinates gives widths proportional to $\epsilon$ and $\epsilon|\lambda_u|^{-(n-1)}$. Its normalized <Haar measure> is therefore proportional to $\epsilon^2|\lambda_u|^{-(n-1)}$, uniformly in the centre. Maximal <separated sets> cover by radius-$\epsilon$ <Bowen balls> and pack disjoint radius-$\epsilon/2$ <Bowen balls>, so their exponential growth rate is $\log|\lambda_u|$. Smallness of $\epsilon$ must exclude nonzero lattice jumps between successive lifted iterates; this is essential to the ball-volume argument.
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